The bigger the distance a carnivore covers in the wild, the more likely it is to suffer stress symptoms in a zoo, say Oxford University scientists.
Polar bears have struggled in many zoos
Stress can show itself in repetitive pacing and in high infant death rates.
The researchers say their work gives the lie to the theory that the captive animal's inability to hunt is the reason for its abnormal behaviour.
"Rather it is the variety of day-to-day life that probably is missing in the zoo," says Dr Georgia Mason.
Her study suggests the husbandry methods that make captive carnivores work for their food - such as hiding meat in containers or moving it so it has to be chased - may not help matters greatly unless they are varied or supplemented with other "environmental enrichments", too.
Dr Mason and her colleague Dr Ros Clubb have analysed at least 30 years of scientific data to write a report for the journal Nature. They took three years themselves to complete the assessment, looking through over 1,200 articles and papers.
They considered 35 captive species, from lions and tigers to mink and foxes, and compiled information on infant mortality and on which animals paced back and forth - behaviour generally regarded as abnormal and a sign that a creature lacks stimulation in its enclosure.
The report concludes that animals that range over larger distances in the wild show higher rates of these stress-related phenomena - the polar bear being the prime example.
Its typical enclosure is about one-millionth the size of its minimum home-range area.
"For a good while people have thought that animals pace up and down before they are fed because this represents hunting behaviour.
"But if you look at which animals spend a lot of time hunting in the wild, this is not a good predictor of pacing. Home range is the key," Dr Mason told BBC News Online.
Grizzly bears do much better
"Stress-related behaviours are predicted by the daily distances an animal would move in the wild and the size of the area it would travel over the course of a year."
And, Mason and Clubb believe it is not so much the actual length of the journey - because even pacing in an enclosure an animal can cover impressive distances - rather it is the stimulation the animal receives on the wild walk that is all important.
"This explains why some hunters such as grizzly bears do really well in zoos - the smallest home ranges we found for them were half a square kilometre."
The scientists' work was part funded by a number of British Zoos keen to learn more about how best to handle the animals in their care.
The Federation of Zoos welcomed the study, although at the same time it urged careful interpretation of some of the findings and took issue with others.
"The research suggests that large carnivores with large home ranges show a higher frequency of stereotypic behaviour such as pacing in captivity," said federation director Dr Miranda Stevenson.
"It does not however say that large carnivores are more likely to show stereotypic behaviour, but when they do this is positively correlated with home-range/body weight. Within a species, some individuals pace while others do not."
Dr Stevenson also questioned the assertion that some enrichment schemes might not be very successful.
"Studies that have been carried out in zoos on the same animals in different environments show that changes in feeding regimes - feeding more often at unpredictable times, etc - significantly reduce pacing, as does increasing the size and complexity of the enclosure; complexity of the environment being as, if not more, important as size."
Dr Mason responded: "We know that these type of approaches work, at least in the short term.
"But what out studies add is that we should all be rather less hung up on hunting, or on making environments complex and then leaving them unchanged for the rest of an animal's life.
"Instead, we should think more creatively about adding the day-to-day changes in stimulation and changes in scene that a wide-ranging carnivore would get in the wild."